This Week’s Topics  Review Class Concepts -Auctions, continued -Repeated Games -Bertrand Trap & Anti-Trust -Auctions

Class Concepts – Auctions  Auctions -One-time auction for a single item -English Auction – Ascending bid auction. The item goes to the last party to bid. -Strategy: When to drop out  What is your WTP? -Dutch Auction – Descending bid auction. The item goes to the first party to bid. -Strategy: When to start bidding  What is your WTP? -First-Price Sealed Bid – All interested parties submit a price. The item goes to the party with the highest bid, at the price he/she submitted. -Strategy: What price to submit  Survey the competition -Second-Price Sealed Bid – All interested parties submit a price. The item goes to the party with the highest bid, at the price of the second highest bid submitted. -Strategy: What price to submit  Survey the competition

Class Concepts – Auctions  Auction Strategies and Terms -For the English Auction and Second-Price Sealed Bid – Bid your willingness to pay! -English Auction Dominant Strategy – Drop out when the bidding exceeds your WTP -Second-Price Sealed Bid Dominant Strategy – Write down and submit your WTP -For the Dutch Auction and First-Price Sealed Bid – Bid below your willingness to pay! -There is no dominant strategy -Your strategy depends on what you believe your competitors are willing to pay -If all bidders are risk neutral then all four bidding rules produce the same expected revenue to the seller. -Private Value (certainty) – You know the value of the auction with certainty. Your value is independent of others’ value. You want to win the auction at any price less than your value. (For Dutch & First-Price Sealed Bid, more bidders  shade less) -Common Value (uncertainty) – You do not know the actual value of the auction (you have an estimate or expected value). The actual value to the item is estimated by all participants. Regardless of auction type: -Your dominant strategy changes and you should shade your bid to avoid the winner’s curse: More bidders  shade more -Learn all you can about your competitor’s WTP. You are all estimating the same value and your bids should be distributed around that value. Your goal is not winning the auction, you want to avoid paying more than the item is worth.

Class Concepts – Auctions  Auctions -So, in summary… -Problem Set 5, Question 2 -a) Certain your profits are $2M, second price sealed bid  Bid your WTP -b) Under second price sealed bid, no benefit from knowing your opponents’ WTP -c) With first price sealed bid, you would benefit from knowing your opponents’ WTP -d) Uncertain profits are $2M, you should shade your bid to avoid the winners’ curse -e) You would benefit from knowing your competitors WTP because you could estimate profits better.

Class Concepts – Repeated Games  Repeated Games -Repeated Games are those with simultaneous decisions over an infinite number of interactions or no known ending point. -Games with simultaneous decisions and a finite number of interactions are sequential games. They should be solved using backward induction, and not the strategies discussed here.  Strategies for Repeated Games -Goal: Sustain price moderation (and higher payoffs) to both firms, even though this is not an equilibrium solution to the simultaneous game -Grim Strategy – Price at the optimal industry price. If an opponent cheats and prices lower, punish them by pricing at marginal cost forever. -t-period Trigger Strategy – Price at the optimal industry price. If an opponent cheats and prices lower, price at marginal cost for the next “t” periods. Then return to the optimal industry price. -Tit for Tat Strategy – Price at the optimal industry price. If an opponent cheats and prices lower, then price at marginal cost in the subsequent period.

Class Concepts – Repeated Games  Repeated Game Strategy Evaluation -Let High Profits = H, Low Profits = L, Cheat Profits = C -Discount = r -Grim Strategy  If both choose this strategy, is it an equilibrium? Will parties want to cheat? -Profits from Both Pricing High = H/(1+r) + H/(1+r) 2 + H/(1+r) 3 + … = H/r -Profits for a Cheater = C/(1+r) + L/(1+r) 2 + L/(1+r) 3 +… = (C + L/r)/(1+r) -If H/r > (C + L/r)/(1+r), then both parties pricing high using the Grim Strategy is an equilibrium. Otherwise, parties have incentive to cheat, and pricing high will not be sustainable. -t-period Trigger Strategy  If the Grim strategy won’t work, this won’t work. If the Grim strategy does work, how many periods will you need to punish your opponent to get them to price high/not cheat? -Profits from Both Pricing High = H/(1+r) + H/(1+r) 2 + … + H/(1+r) t+1 -Profits for a Cheater = C/(1+r) + L/(1+r) 2 + L/(1+r) 3 +… + L/(1+r) t+1 -If the profits from both pricing high for the first t+1 periods are better than the cheating profits for the same periods, then the t-period trigger strategy is an equilibrium. Otherwise, parties have an incentive to cheat, and this strategy will not be sustainable.

Class Concepts – Repeated Games  Knowledge Check -Two firms can receive $8M in profits each if they both price high. If one of them decides to price lower, that firm will receive $15M in profits that period and the other firm will receive $0 in profits. If both firms price low they will receive $4M in profits each. Use a 10% discount rate. -1) Is the grim strategy effective?

Class Concepts – Repeated Games  Knowledge Check -Two firms can receive $8M in profits each if they both price high. If one of them decides to price lower, that firm will receive $15M in profits that period and the other firm will receive $0 in profits. If both firms price low they will receive $4M in profits each. Use a 10% discount rate. -1) Is the grim strategy effective? -Profits from Pricing High = $8M/0.1 = $80M -Profits from Cheating = $15M/1.1 + ($4M/1.1 + $4M/ …)/1.1 -Profits from Cheating = ($15M + $4M/.1)/1.1 = $50M -Yes, the grim strategy for both parties is an equilibrium. -2) Is the t-period trigger strategy effective for t = 2? For t = 3?

Class Concepts – Repeated Games  Knowledge Check -Two firms can receive $8M in profits each if they both price high. If one of them decides to price lower, that firm will receive $15M in profits that period and the other firm will receive $0 in profits. If both firms price low they will receive $4M in profits each. Use a 10% discount rate. -2) Is the t-period trigger strategy effective for t = 2? For t = 3? -For t = 2  No, the t-period trigger strategy is not an equilibrium for the game -Profits from Pricing High = $8/1.1 + $8/ $8/1.1 3 = $19.89M -Profits from Cheating = $15/1.1 + $4/ $4/1.1 3 = $19.94M -For t = 3  Yes, the t-period trigger strategy is an equilibrium -Profits from Pricing High = $8/1.1 + $8/ $8/ $8/1.1 4 = $25.36M -Profits from Cheating = $15/1.1 + $4/ $4/ $4/1.1 4 = $22.68M -So, you should price low for at least 3 periods to “punish” your opponent for cheating to make price moderation behavior the dominant strategy.

Class Concepts – Bertrand Trap & Anti-Trust  How to escape the Bertrand Trap -Product Differentiation -Consumer Switching Costs -Consumer Search Costs -Long-run price moderation & punishment -These are the strategies we just discussed, known as tacit collusion) -Limiting capacity -This shows a commitment to higher prices, and is another type of tacit collusion -Rebates (from toy car game)  Anti-Trust -Price Fixing is illegal! -“Efforts” to facilitate price moderation are illegal

Class Concepts – Principal-Agent Problems  Safelite Auto -Principal may be Safelite management -Agent is a Safelite employee -How can you align the incentives of the agent with those of the principal?  Economics of Networks -Positive Network Externality: The value of a network to an individual increases as more people join the network. -Establishing a new network is difficult as it is difficult to reach critical mass/tipping point -Target early adopters, large users and be prepared to subsidize those who switch or build complements for your network -Establish control over access to the network -If it is difficult or costly for users of the network to participate in multiple networks, these can be winner-take-all markets